When it comes to gender roles there is much variety and complexity in the world. Regardless of the rationalising advances of modernity rich embedded cultures and realities exist in contrast to the narrow history you present which is chiefly a feature of Western and capitalistic oriented nations.It depends on what your definition of independent is.
Biologically women tend to have a drive to tie a man down as in the past women needed men to survive, to protect them and to provide resources for children. While the alpha just sought to impregnate as many women as he could. So their is a fundamental disconnect in the desires between men and women. Men seek independence and women seek security.
But society has changed dramatically over time women have reached more-or-less the same level as men in society. They can work so don't need a man to survive, they don't need a man to protect them as this is meant to be a service provided for by the state and they are able to raise children either with their own money or government handouts. The result is that men have become less valuable to women. In the past it was most important that a man could provide for a woman. Now that young women earn about the same as men, they have become more demanding. They generally still want wealthy men, but now they also want attractive men, men with good bodies, men with the same interests etc.
This, in combination with female supremacism (feminism), as opposed to women's rights advocacy, has led to the growing phenomena of men seeking women from poorer countries as they can no longer get the women they think they deserve from Western societies - very attractive; and males withdrawing from society, playing videos games in a basement all day because they are seen as lower value and been told they are useless. The MGTOW movement you mention is another symptom of these changes. Whereby men cut themselves off from relationships with women as they think they are not worth the hassle. Or at least that is what they say. For me, MGTOW more represents men who are unhappy with the new gender playing-field, don't think they can get what they want, are not willing to put in the effort and have maybe had a bad experience with women; really they would probably like a healthy relationship, but have chosen to act like a sulky child and seal themselves off. I think it is a form of self harm. I doubt they will be happy in their 50s and 60s as MGTOW.
Men and women need to come to compromised agreements in their relationships. If a man seeks some sort of independence, but the woman want to be very close, then they need to find a solution that is acceptable for both.